The subject matter of the present invention relates to a workstation based software method and apparatus, which is responsive to seismic data and well log data received from an earth formation in response to a seismic operation, for gridding the earth formation by generating a "structured" grid and imposing that "structured grid" on the earth formation. Since the structured grid is comprised of a plurality of grid blocks, when the structured grid is imposed on the earth formation, the workstation based software method and apparatus further generates a plurality of more accurate information corresponding, respectively, to the plurality of grid blocks of the structured grid. The plurality of more accurate information relates, for example, to the transmissibility properties of the plurality of grid blocks of the structured grid. The plurality of more accurate information is provided as an input to a conventional workstation based software "reservoir simulator". In response to the plurality of more accurate information, the "reservoir simulator" generates a corresponding plurality of simulation results (such as pressures and saturations) pertaining, respectively, to the plurality of grid blocks of the structured grid, the plurality of simulation results being overlayed, respectively, upon the plurality of grid blocks of the structured grid so that a new simulation result is associated with each grid block of the structured grid. The grid blocks of the structured grid and the new simulation results associated with each grid block are displayed on the workstation display monitor for viewing by an operator of the workstation.
More particularly, the subject matter of the present invention relates to an improved "structured" gridder software for use within a simulation gridding program, the simulation gridding program being hereinafter called "Flogrid". The "structured" gridder software, disposed within the "Flogrid" simulation gridding program, is adapted to be executed by the workstation processor; When executed by the workstation processor, the "structured" gridder software will ultimately generate the above referenced "more accurate earth formation grid block property information". This "more accurate grid block property information" is used by a reservoir simulator software for generating the "more accurate simulation results", such as pressures and saturations, that are displayed on the workstation display monitor.
Seismic operations are performed near one or more wellbores in an earth formation, and a plurality of seismic data are obtained from such seismic operation. In addition, well logging operations are also performed in the one or more wellbores and well log data is also obtained from the well logging operations. The seismic data and the well log data are input to a computer workstation where an interpretation program is executing. The interpretation program of the prior art was comprised of a first program sometimes called "grid" which generated data, and a second simulation program, responsive to the first program, which received the data from the first "grid" program and generated a set of simulation results and displayed the simulation results on the workstation display, the displayed simulation results enabling an operator to determine the flow properties of the earth formation situated near the one or more wellbores drilled into the formation. In particular, the first "grid" program establishes a grid for each horizon in the earth formation near the wellbores, the grid for each horizon comprising a multitude of individual cells. In addition, the first "grid" program generates data and other information for each of the individual cells for each horizon, the data and other information for each cell being transmitted to the second simulation program which uses the data and information for each grid cell, received from the first grid program, to generate a set of simulation results for each cell of the grid. A simulation result is displayed on the workstation display for each cell of the grid thereby enabling an operator of the workstation to determine the flow producing properties of each of the cells in the gridded earth formation located near the wellbores.
However, continuous developmental efforts are focused on improving the quality and accuracy of the data and other information generated by the first "grid" program. When a set of improved and more accurate data is received by the second simulation program, the simulation function practiced by the second simulation program will be more accurate and complete; and, as a result, the simulation results generated by the second simulation program will be more accurate and complete. Consequently, in view of the more accurate and complete set of simulation results (e.g., pressures and saturations) generated by the second simulation program, the flow properties associated with each cell or grid block of the grid imposed on the earth formation located near the wellbores can be more accurately determined. Consequently, a need exists to improve the first "grid" program so that more accurate data is generated by the first grid program.
Computer simulation of physical processes using partial differential equations requires a tessellation of a specified volume of space into a set of small blocks. Such tessellations can be of various types:
1. "Structured" grids which are either rectangular or "tartan grids" or distorted versions of these; PA1 2. "Semi-structured" grids, in which the domain is first split into an unconstrained set of sub-domains and a structured grid is placed in each one; PA1 3. "Unstructured" grids which consist of arrangements of triangles in 2D space or tetrahedra in 3D space; and PA1 4. "Structured-unstructured" grids in which the domain is first split into an unconstrained set of sub-domains and structured grids are placed in some sub-domains and unstructured grids placed in others.
Most of the grid generation methods in use today have been developed in the area of computer aided design, in particular the aerospace industry.
However, in connection with the "Unstructured" grids, flow simulations on grids based on triangles (that is, for "Un-structured" grids) have been used by various authors inside and outside the petroleum industry. Control volumes have been formed around each node of a triangular grid by joining the edge midpoints to the triangle centroids for solving a 2D) magnetostatic problem. This technique is commonly known as the control volume finite element (CVFE) method. In addition, control volumes have been formed by joining the perpendicular bisectors of triangle edges of a Delaunay triangulation for solving semiconductor device equations. This technique has been applied to reservoir simulation, which is known as the PEBI or the Voronoi method. Heterogeneous problems have been handled by defining permeability to be constant over a triangle. An alternative difference scheme has been used based on the CVFE method in which permeabilities are defined to be constant within control volumes. This approach handles boundaries of layers with large permeability differences better than the traditional CVFE method and as with the traditional method it leads to a multi-point flow stencil, hence referred to as an MPFA scheme. By contrast, the PEBI method reduces to a two point flow stencil. The PEBI method has been extended to handle anisotropic heterogeneous systems by defining permeability to be constant within a triangle and by adjusting the angle between triangle edges and cell boundaries. This approach has two problems; firstly handling layers of contrasting permeabilities is poor, secondly in highly anisotropic systems the angle condition between triangle edges and cell boundaries may become so severe that cells begin to overlap. As an alternative to using control volumes formed around nodes of triangulations, it is possible to use the triangles themselves as control volumes. A drawback of triangular control volumes compared to Voronoi volumes is the much higher number of cells in the former; for random point distributions an average factor of two and five exist in two and three dimensions respectively. An advantage of triangular grids is the flexibility in honoring complex geological and production features.
An improved "Unstructured" gridder software is disclosed in a prior pending U.S. patent application Ser. No. 08/873,234 filed Jun. 11, 1997 and entitled "Method and Apparatus for generating more accurate earth formation grid cell property information for use by a simulator to display more accurate simulation results of the formation near a wellbore" to Dayal Gunasekera (hereinafter called, the "Gunasekera specification"), the disclosure of which is incorporated by reference into this specification.
The "Flogrid" simulation gridding program of the present invention disclosed in this specification includes: (1) the "Unstructured" gridder software disclosed in the Gunasekera specification, and (2) an improved "Structured" gridder software in accordance with the present invention which further includes a novel "structured areal gridder" software in accordance with the present invention.
Traditionally, geological models have consisted of maps, and, given a geological model, a simulation model was constructed from the geological model. However, in the prior art, reservoir engineers would directly modify the simulation model rather than update the underlying geological model. Today, there is a growing demand for a better and more integrated approach to reservoir modeling. The improved "structured" gridder software in accordance with the present invention supports the iterative process of modifying the underlying geological models and then propagating the modifications to the simulation model more quickly than is currently possible.
Many different algorithms have been proposed to perform the gridding task automatically. In practical use, there are two main classes of prior art gridding algorithms: (1) Algebraic methods in which an interpolation formula is used to interpolate the boundary curves; these can work well if the region is not too distorted; and (2) Methods based on the solution of partial differential equations. The best methods of this class solve a diffusion type equation based on transforming Laplace's equation on the physical space to a nonlinear problem in the logical space. Some variants of this approach produce good quality grids, but can suffer from inside-out cells near sharp bends in the boundary. All of these methods require the user to fix the distribution of the grid points on the boundary of the region.